Does mean of uncountable infinite equal to infinite, which is known in calculus? [duplicate]

As I understand, the number of all infinite lentgh sequences which is consist of $$\left\{1,2\right\}$$ is uncountable. I want to learn, Does mean of uncountable infinite equal to infinite, which is known in calculus?

I mean for example,

Let, $$N$$ be a number of all infinite lentgh sequences which is consist of $$\left\{1,2\right\}$$.

Then, can we say ?

$$\lim_{n\to\infty} \frac{N}{2^n}=1$$

No, these are completely different concepts. $$N$$ is not a number. There is no such thing as the "number of all infinite length sequences of $$\{1,2\}$$. What you could talk about is the cardinality of the set of all infinite length sequences of $$\{1,2\}$$.

However, if you define $$N$$ to be a cardinality, then the expression $$\frac{N}{2^n}$$ is undefined, and thus the limit you are asking for does not exist.

• I mean for example, $n=5$. We have $2^5$ possible finite sequence. Then if $n\to\infty$?
– user548054
Jul 1, 2019 at 7:16
• @Elementary If $n=5$, then the expression $\frac{N}{2^5}$ is nonsensical.
– 5xum
Jul 1, 2019 at 7:18
• math.stackexchange.com/q/3286436/548054
– user548054
Jul 8, 2019 at 9:05